MA 125 Midterm: ma125-ct-fall-2016-test-2
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Show all your work, simplify and justify your answer! No partial credit will be given for the answer only! All problems in part i are 8 points each: find the derivative of the function f (x) = tan(x3), find the derivative of the function f (x) = (cid:0) x+1 x 1(cid:1)4. 2: find the absolute maximum and minimum of the function f (x) = x3. 12x on the interval [ 1, 3]: verify that the conditions of the mean value theorem hold. Next nd the number c which satis es the conclusion of the mean value theorem for the function f (x) = x3 + x on the interval [0, 1]. 4: show that the equation f (x) = x9 + 35 + x + 3 = 0 has exactly one solution and. Hint: rst show that there is at least one solution. Next show that two distinct solutions is impossible.